There's a grassy field. 11 goats on the field will eat all the grass in seven days and then starve. 10 goats would finish all the grass in 8 days and then starve. How long could three goats survive on the field?

While I solved this a complicated mathematical way, there's also a simpler mathematical way to solve it:

In the first scenario there are 77 goat days of food. In the second case, there is 80 goat days. Therefore the field produces enough grass each day to sustain 3 goats, and so the 3 goats could live there forever.